1. Field of the Invention
The present invention relates to a method for determining an optimum sampling frequency to be performed by a power analyzer, more particularly to a method for determining an optimum sampling frequency for a power analyzer by referring to a V-curve plot.
2. Description of the Related Art
In the field of measurement of an electrical power system, important digital signal processing operations include measurement of a magnetic field, measurement of a non-linear load, measurement of harmonics, etc. The measurement of harmonics can be applied in analyses of amplitudes, phases, real power, reactive power, apparent power, equivalent impedance and total harmonic distortion. Various commercial harmonic measuring devices are in the market heretofore for different purposes, such as:
a spectrum analyzer for analysis of harmonic components;
a harmonic analyzer for analysis of amplitudes of harmonics;
a distortion analyzer for analysis of total harmonic distortion; and
digital harmonic measuring equipments using a digital wave filter and Fast Fourier Transform (FFT) for rapid acquisition of a measuring signal on large scale, and cooperating with a personal computer real time analysis of the signal.
Discrete Fourier Transform (DFT) can be used to transform a time domain signal to a frequency domain signal to obtain a frequency spectrum. In the frequency spectrum, components of different frequencies are separated, and the frequency domain signal is a combination of a plurality of independent components. The frequency spectrum can show important information that cannot be acquired via the time domain signal, and therefore a complex system can be processed and parameters of the time domain signal can be obtained via the frequency spectrum. With the development of FFT, it takes a relatively short time to transform a time domain signal to a frequency domain signal. Therefore, FFT is most commonly used in analyses of harmonics.
However, FFT has limits in actual applications, and a digital signal is sampled randomly, so an error will occur due to limitations of FFT. The most common effects are a picket-fence effect and a leakage effect attributed to a sampling frequency that is not an integral multiple of a frequency of an original signal.
The aforementioned picket-fence effect is attributed to harmonic frequencies that do not match with graduations of the frequency spectrum. On a premise of an accurate analysis, characteristics of the time domain signal cannot be changed to conform with the graduations of the frequency spectrum. A sole method available for enabling an accurate analysis is to shift the graduations of the frequency spectrum to conform with the characteristics of the time domain signal. A shift in the graduations of the frequency spectrum can be achieved by changing the sampling frequency or a number of sample points. Commonly, the number of sample points is 128 and the sampling frequency is 128*60 (data/sec) for obtaining a sampling signal of a system with a frequency of 60 Hz. There are two problems when changing the number of sample points for shifting the graduations of the frequency spectrum. First, when the number of sample points is not 2r (wherein r is a positive integer), FFT cannot be used, and only DFT can be used for transforming the sampling signal of the system to the frequency domain signal. Therefore, it takes a relatively long time for computing. Second, on the aforementioned conditions of the sampling signal, an increase/decrease of one in the number of sample points causes an approximate decrease/increase of 0.5 Hz in the graduations of the frequency spectrum correspondingly. This quantity is much greater than a variation of frequencies of an electrical power system in normal operation. Therefore, it is more practical to change the sampling frequency for shifting the graduations of the frequency spectrum.
There are two problems when changing the sampling frequency and re-sampling the original signal. If the original signal is not one stored in a digital system, it will be needed to ensure that characteristics of a re-sampling signal conform with those of the previous sampling signal when re-sampling. It is difficult to achieve this condition. If the original signal is one stored in a digital system, data of the digital signal will be discrete. When re-sampling discrete data, it is needed to use a numerical method to acquire new data. This method will cause an error, but can ensure that the characteristics of the re-sampling signal conform with those of the previous sampling signal when re-sampling. The present invention utilizes Lagrange's interpolation method to solve the problem attributed to re-sampling discrete data.